How can I find the equation for the radius of a 'racing circle' (the
fastest path a racecar can take through the corner defined by the
quadrants of two circles), an arc sandwiched between identical quadrants
of two concentric circles?

Two vehicles are travelling at 60 mph. One is a 50-foot flatbed truck
with a drive-on ramp lowered down to the roadway. The second is a rear
wheel drive sedan only 3 feet directly behind the flatbed truck. It is
capable of coming to a complete stop from 60 mph in 120 feet. The truck
slows to 59 1/2 mph. Since the car is gaining on the truck at a rate of
1/2 mph, the front wheels of the car begin to slowly move up the ramp.
Question: When the rear tires finally make direct contact with the ramp,
will the car, which was moments ago traveling at 1/2 mph relative to the
truck's ramp, suddenly go from 1/2 mph ramp speed to 60 mph ramp speed
and thus crash into the back of the truck's cab section?

If temperature is the total amount of kinetic energy possessed by the
particles in a given substance, and special relativity holds that
nothing can move faster than the speed of light, does that mean that
there is an upper limit for how hot a substance can become (e.g. the
temperature where the particles begin to move at the speed of light)?

I am trying to create a chart that could be used to help determine
what weight of methanol/water to use to either raise or lower the
specific gravity of a volume of corrosion inhibitor in bulk mixing
tanks.

Joe and Harry have been assigned the task of peeling potatoes. Joe is
given 40 kg of potatoes, which average 1 kg in size, while Harry is
given 20 kg of potatoes, which average 0.5 kg in size. Assuming that
Joe's and Harry's peeling skills are equal, and if Joe finishes his
task in one hour, how long will it take Harry to accomplish his task
and why?